Question

Calculate the slope of a line that is perpendicular to the one shown in the graph.
The line has two points and goes through each of them. The coordinates of each point are, (3, 0) and (0, 6)

Answer 1

To find the slope of a line that is perpendicular to the line defined by the points (3, 0) and (0, 6), we first need to calculate the slope of the given line.

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (3, 0) \((x_1, y_1)\) and (0, 6) \((x_2, y_2)\):

- \(x_1 = 3\), \(y_1 = 0\)
- \(x_2 = 0\), \(y_2 = 6\)

Substituting into the formula:

\[
m = \frac{6 - 0}{0 - 3} = \frac{6}{-3} = -2
\]

The slope of the line through the points (3, 0) and (0, 6) is \(-2\).

Next, the slope of a line that is perpendicular to another line is the negative reciprocal of the original slope.

To find the negative reciprocal of \(-2\):

1. Take the reciprocal: \(\frac{1}{-2} = -\frac{1}{2}\)
2. Change the sign to get the negative reciprocal: \(\frac{1}{2}\)

Therefore, the slope of the line that is perpendicular to the one shown in the graph is:

\[
\frac{1}{2}
\]